Question

The function fx) changes value when x changes from xo to xo+ dx. Find the approximation error lAf-dfl. Round your answer, if appropriate. f(x) = x², x 0-6, dx = 0.06

Answer 1

The approximation error |Δf-Δx| for the given function f(x) = x² and xo = 0.06 is 0.1404.

Step-by-step explanation:

The function f(x) changes value when x changes from xo to xo+dx. To find the approximation error |Δf-Δx|, we need to find the difference between f(x+dx) and f(xo). In this case, f(x) = x² and xo = 0.06.

To find f(x+dx), we substitute x+dx into the function: f(x+dx) = (x+dx)²

So, f(x+dx) = (0.06+0.06)² = 0.144.

To find f(xo), we substitute xo into the function: f(xo) = (0.06)² = 0.0036.

Therefore, the approximation error |Δf-Δx| is |0.144-0.0036| = 0.1404.